This paper investigates the relationship between democracy and economic growth in the context of a linear index threshold regression model. We first introduce the baseline model with endogeneity and propose a two-step smoothed GMM estimation method. We establish the consistency and derive the asymptotic distributions of the proposed estimators. We then extend the approach to a dynamic panel context and employ the model to explore the impact of democratization on economic growth. Our findings reveal that democratization’s impact on growth is nonlinear and depends on the country’s current institutional quality level. Furthermore, democracy’s impact on economic growth is more pronounced in countries with higher education levels than others, suggesting that education also plays a crucial role in enhancing the positive effects of democracy. Our proposed estimator can be used in other situations that require the use of more than one threshold variable. In these cases, our hybrid estimator has less stringent data requirements than an alternative model where the thresholds would enter separately, especially when the threshold variables are correlated.

中文翻译：

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阈值非线性和民主与增长的关系

本文在线性指数阈值回归模型的背景下研究了民主与经济增长之间的关系。我们首先引入具有内生性的基线模型，并提出一种两步平滑 GMM 估计方法。我们建立一致性并推导所提出的估计量的渐近分布。然后，我们将该方法扩展到动态面板环境，并利用该模型探索民主化对经济增长的影响。我们的研究结果表明，民主化对增长的影响是非线性的，并且取决于国家当前的制度质量水平。此外，民主对经济增长的影响在教育水平较高的国家比其他国家更为明显，这表明教育在增强民主的积极影响方面也发挥着至关重要的作用。我们提出的估计器可以用于需要使用多个阈值变量的其他情况。在这些情况下，我们的混合估计器的数据要求不如单独输入阈值的替代模型严格，尤其是当阈值变量相关时。